Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations

On the macroscopic response and field statistics in particulate composites with elasto-plastic phases and random microstructures

In this article, we carry out a theoretical investigation of the macroscopic response and field statistics in two-phase particulate composites with elasto-plastic constituents and random microstructures under cyclic loading conditions. To this end, we make use of the “incremental variational homogenization” (IVH) procedure of Agoras et al. (2016, “Incremental Variational Procedure for Elasto-Viscoplastic Composites and Application to Polymer- and Metal-Matrix Composites Reinforced by Spheroidal Elastic Particles,” Int. J. Solid Struct., 97-98, pp. 668-686) and corresponding unit cell finite element simulations. Results are obtained for statistically isotropic distributions of spherical particles and for “spheroidal distributions” of spheroidal particles. It is shown analytically that the IVH estimate of Agoras et al. and that of Lahellec and Suquet (2013, “Effective Response and Field Statistics in Elasto-Plastic and Elasto-Visco-Plastic Composites Under Radial and Non-Radial Loadings,” Int. J. Plasticity, 42, pp. 1-30) are equivalent. In addition, it is illustrated by means of specific numeral comparisons that the IVH estimate is also equivalent (to within numerical accuracy) to the corresponding estimates of Idiart and Lahellec (2016, “Estimates for the Overall Linear Properties of Pointwise Heterogeneous Solids With Application to Elasto-Viscoplasticity,” J. Mech. Phys. Solids, 97, pp. 317-332) and Lucchetta et al. (2019, “A Double Incremental Variational Procedure for Elastoplastic Composites With Combined Isotropic and Linear Kinematic Hardening,” Int. J. Solid Struct., 158, pp. 243-267). Furthermore, it is shown in the context of specific exact results for composite materials with lamellar microstructures that the elastic-plastic coupling and the Bauschinger effect are the macroscopic manifestations of the incompatibility of the local elastic strains. Local strain hardening is incorporate in the IVH model. The predictions of the IVH model for the macroscopic response of particulate composites are found to be in good agreement with the corresponding numerical results, in general. For the extreme cases of rigidly reinforced composites and porous materials, however, the IVH model fails to capture the elastic-plastic coupling and the Bauschinger effect. The underlying reasons for this shortcoming are discussed and a strategy toward the improvement of the IVH model is proposed. © 2021 by ASM

A homogenization model of the Voigt type for skeletal muscle

International audienceA three-dimensional constitutive model for skeletal muscle incorporating microstructural characteristics is developed and numerically implemented in a general purpose finite element program. The proposed model takes into account explicitly the volume fractions of muscle fibers and connective tissue by using the Voigt homogenization approach to bridge the different length scales of the muscle structure. The model is used to estimate the active and passive homogenized muscle response. Next, the model is validated by experimental data and periodic three-dimensional unit cell calculations comprising various fiber volume fractions and mechanical properties of the constituents. The model is found to be in very good agreement with both the experimental data and the finite element results for all the examined cases. The influence of fiber volume fraction and material properties of constituents on effective muscle response under several loading conditions is examined

Incremental variational procedure for elasto-viscoplastic composites and application to polymer- and metal-matrix composites reinforced by spheroidal elastic particles

This paper presents an alternative formulation of the incremental variational procedure (IVP) of Lahellec and Suquet (2013) to estimate the macroscopic response and field statistics in elasto-viscoplastic composites. The basic idea is to make use of a time-incremental variational formulation for the strain-rate potential of the elasto-viscoplastic composite, to define a homogenization problem for a viscoplastic composite with non-uniform “eigenstrain rates” in the phases. Both the nonlinearity and the heterogeneity of the properties in the phases can then be handled by means of the variational procedure of Ponte Castaneda (1992) in terms of a suitably optimized linear comparison composite with uniform properties, for which standard homogenization estimates are available. The IVP is then applied to two-phase composites consisting of aligned, ellipsoidal elastic particles in an elastic-ideally plastic matrix and the effects of the particle concentration and shape, as well as the properties of the matrix and particles, are investigated. Upon uniform strain-rate loading, three regimes of deformation are observed: a linear, purely elastic regime, followed by a transient elasto-plastic regime, and then a steady-state ideally plastic regime. It is found that the more compliant the matrix and inclusion phases of the composite are, the stronger the long-term memory effects are, especially when the inclusions are more compliant than the matrix. Similarly, the duration of the transient regime is significantly extended for sufficiently elongated, or flattened particle shapes, but only under certain modes of deformation. Finally, consistent with earlier work, significant Bauschinger effects are observed for cyclic loading conditions. © 201

A homogenization model of the Voigt type for skeletal muscle

A three-dimensional constitutive model for skeletal muscle incorporating microstructural characteristics is developed and numerically implemented in a general purpose finite element program. The proposed model takes into account explicitly the volume fractions of muscle fibers and connective tissue by using the Voigt homogenization approach to bridge the different length scales of the muscle structure. The model is used to estimate the active and passive homogenized muscle response. Next, the model is validated by experimental data and periodic three-dimensional unit cell calculations comprising various fiber volume fractions and mechanical properties of the constituents. The model is found to be in very good agreement with both the experimental data and the finite element results for all the examined cases. The influence of fiber volume fraction and material properties of constituents on effective muscle response under several loading conditions is examined. © 2016 Elsevier Lt

Constitutive modeling and finite element methods for TRIP steels

A constitutive model that describes the mechanical behavior of steels exhibiting "TRansformation Induced Plasticity" (TRIP) during martensitic transformation is presented. Multiphase TRIP steels are considered as composite materials with a ferritic matrix containing bainite and retained austenite, which gradually transforms into martensite. The effective properties and overall behavior of TRIP steels are determined by using homogenization techniques for nonlinear composites. A methodology for the numerical integration of the resulting elastoplastic constitutive equations in the context of the finite element method is developed and the constitutive model is implemented in a general-purpose finite element program. The model is calibrated by using experimental data of uniaxial tension tests in TRIP steels. The problem of necking of a bar in uniaxial tension is studied in detail. The constitutive model is used also for the calculation of "forming limit diagrams" for sheets made of TRIP steels; it is found that the TRIP phenomenon increases the strain at which local necking results from a gradual localization of the strains at an initial thickness imperfection in the sheet. © 2005 Elsevier B.V. All rights reserved

Fiber plasticity and loss of ellipticity in soft composites under non-monotonic loading

In this work, we relate fiber plasticity in soft composites to the loss of ellipticity of the governing equations of equilibrium of a composite under non-monotonic uniaxial loading. The loss of ellipticity strongly indicates the emergence of localization phenomena in the composite, reminiscent of the emergence of kinking instabilities in tendon, which occur as a response to tendon “overload” without requiring any macroscopic compressive loading. We examine soft composites where both fibers and matrix can be highly extensible and plastic deformations are present in the fiber phase. We first propose a transversely isotropic constitutive model for the fibers allowing for plastic deformations, taking into account a single slip direction, consistent with the microstructure of hierarchically assembled collagen fibers. Following, we propose a simple hyperelastic model for the matrix and combine the two following the Voigt assumption. We then formulate a general loss of ellipticity criterion for an elastoplastic material subjected to finite deformations. We use this criterion to indicate critical conditions for loss of ellipticity in the soft composite and individually in the fiber phase, under various loading–unloading paths. Results show that plastic deformation of the fiber phase during tensile loading can lead to ellipticity breakdown during elastic unloading while, macroscopically, the material is still in tension, indicating the possible onset of an instability. © 2022 Elsevier Lt